United have not lifted the trophy since a Cristiano Ronaldo goal and a Ruud van Nistelrooy brace helped them to a 3-0 victory over Millwall at the Millennium Stadium, their first success in the competition since 1999.
Only Ryan Giggs and Darren Fletcher of the present United squad were involved in that record 10th triumph.
It was a point not lost on Sir Alex Ferguson prior to his retirement last summer, and one Cleverley is keen to put right as the team prepare for the visit of Swansea on Sunday.
"The old manager really instilled into us the fact a lot of players in the squad haven't won the FA Cup," said Cleverley.
"Growing up as a lad, the FA Cup final was an iconic thing. The run starts on Sunday and hopefully we can progress."